Finite Group Databasebeta

← #15783788

Subgroups — #15783788

Order 3328.

180 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718114C211yesmaximal, characteristic, complemented
2#13117131C211yesmaximal, characteristic
3#13116962C211yesmaximal, characteristic
4#13116958C211yesmaximal, characteristic
5#13113039C211yesmaximal, characteristic, complemented
6#13113030C211yesmaximal, characteristic, complemented
7C13×#1420C211yesmaximal, characteristic, complemented
8C2×C13×Q32C2211yescharacteristic
9#11718853—21no—
10C2×Dic104C2211yescharacteristic
11#11718562C2211yescharacteristic
12#11718557—21no—
13C13×M64C2211yescharacteristic
14C13×#368C2211yescharacteristic
15#11718157—21no—
16#11718114—21no—
17#11718114—21no—
18#11718098C2211yescharacteristic
19C2×#88034C2211yescharacteristic
20#11718088—21no—
21#11718039—21no—
22D13×C32—21no—
23C2×C13×Q16—21no—
24#88196—41no—
25#88163—41no—
26C2×Dic52—21no—
27#88155D411yescharacteristic
28C13×Q32—21no—
29C13×Q32—21no—
30C2×C13×C16C2311yescharacteristic
31C13×#108—21no—
32#88076—41no—
33#88064—41no—
34#88059—21no—
35#88052D411yescharacteristic
36Dic104—21no—
37Dic104—21no—
38#88038—21no—
39C16×D13—21no—
40C13×C32—21no—
41#88034D411yescharacteristic
42#88034D411yescharacteristic
43#13701—131nomaximal, Sylow
44C2×Q8×C13—41no—
45#6127D811yescharacteristic
46C2×Dic26—41no—
47C13×Q16—41no—
48C13×Q16—41no—
49C13×M16—41no—
50C2×C8×C13C2×D411yescharacteristic
51#6107—81no—
52#6106—81no—
53#6099—41no—
54#6099D811yescharacteristic
55Dic52—41no—
56Dic52—41no—
57Dic52—81no—
58#6095—81no—
59#6094—21no—
60C8×D13—21no—
61C13×C16C2×D411yescharacteristic
62C13×C16#4111yescharacteristic
63#6090—21no—
64C2×Q64—131no—
65#2258—131no—
66#2222—131no—
67#2222—131no—
68#1425—131no—
69#1420—131no—
70#1420D1311yescharacteristic, complemented
71Q8×C13—81no—
72Q8×C13—81no—
73C2×C4×C13—81no—
74C2×C4×C13C2×D811yescharacteristic
75C22⋊D13—21no—
76C2×Dic13—81no—
77D52D1611yescharacteristic
78C4×D13—21no—
79Dic26—81no—
80Dic26—81no—
81Dic26D1611yescharacteristic
82C8×C13—81no—
83C8×C13#12111yescharacteristic
84C8×C13#13511yescharacteristic
85#1055—21no—
86#1055—81no—
87C2×Q32—131no—
88C2×Q32C2×D1311yescharacteristic
89#504—131no—
90#473—261no—
91#473—261no—
92Q64—261no—
93Q64—261no—
94M64—261no—
95M64C2×D1311yescharacteristic
96C2×C32—131no—
97C2×C32—261no—
98#368—131no—
99#368C2×D1311yescharacteristic
100#362—261no—
101#362—261no—
102C22×C13#50811yescharacteristic
103C2×D13—21no—
104C4×C13—161no—
105C4×C13#46611yescharacteristic
106C4×C13C2×D1611yescharacteristic
107Dic13—21no—
108Dic13—161no—
109#137—521no—
110#137—521no—
111C2×Q16—21no—
112C2×Q16—261no—
113#131—131no—
114Q32—21no—
115Q32—21no—
116Q32—261no—
117Q32—261no—
118M32—131no—
119M32—261no—
120C2×C16—261no—
121C2×C16C22×D1311yescharacteristic
122#108—21no—
123#108—261no—
124#101—521no—
125#101—521no—
126C32—21no—
127C32—131no—
128C32—131no—
129C2×C13—21no—
130C2×C13#221511yescharacteristic
131D13—41no—
132#41—131no—
133C2×Q8—41no—
134C2×Q8—521no—
135Q16—41no—
136Q16—41no—
137Q16—521no—
138Q16—521no—
139Q16—1041no—
140Q16—1041no—
141SD16—1041no—
142SD16—1041no—
143M16—41no—
144M16—131no—
145M16—261no—
146M16—521no—
147C2×C8—261no—
148C2×C8D4×D1311yescharacteristic
149C16—261no—
150C16#612711yescharacteristic
151C16D4×D1311yescharacteristic
152C13#1370111yescharacteristic, complemented, Sylow
153Q8—81no—
154Q8—81no—
155Q8—131no—
156Q8—1041no—
157Q8—1041no—
158D4—131no—
159D4—261no—
160C2×C4—81no—
161C2×C4—261no—
162C2×C4—1041no—
163C2×C4D8×D1311yescharacteristic
164C8—81no—
165C8—261no—
166C8—1041no—
167C8#8813811yescharacteristic
168C8#8817011yescharacteristic
169C22—261no—
170C22#1171857711yescharacteristic
171C4—161no—
172C4—261no—
173C4—2081no—
174C4#1171843611yescharacteristic
175C4D13×D1611yescharacteristic
176C2—21no—
177C2—521no—
178C2#1311692111yescharacteristic
subgroupG/H
centerC2#13116921
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC13×#1420C2
socleC2×C13#2215
prime radical#6127D8
hypercenter#1420D13
hypocenterC13#13701
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1420

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11718114C2semidirect
5. #13113039C2semidirect
6. #13113030C2semidirect
7. C13×#1420C2semidirect
70. #1420D13semidirect
152. C13#13701semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117181142
#131171312
#131169622
#131169582
#131130392
#131130302
C13×#14202
#1370113